1. Field of the Invention
The invention relates to instruments for measuring fluid flow through a pipe of conduit, and more particularly to those meters for measuring the flow of gas.
2. Description of the Prior Art
The consumption of natural gas is typically determined by measuring a volume of gas that flows past a certain location in a transmission or distribution pipe during a predetermined time interval. As the cost of natural gas increases, there is a need for more accurate techniques and less expensive equipment for measuring gas flow. Gas flow in small pipes has been measured with orifice metering equipment. In large pipes, multiple orifice metering runs are required to obtain the 0.5% accuracy that is specified by gas companies.
For many years, ultrasonic meters have been used to measure liquid flow in pipes. While this type of meter has provided 0.5% accuracy or better for measuring the flow of liquids, its application to gas is limited to "clean" gases with relatively stable composition that flow in fully developed turbulent flow conditions. At many sites that require flow metering, the gases are dirty, change composition rapidly and do not flow under fully developed turbulent flow conditions. Ultrasonic flow meters have not been able to provide the desired accuracy under such conditions.
A basic technical problem in applying ultrasonics to the measurement of gas flow arises from the different physical properties of liquids and gases. Gas must be transported in large volume due to its lower density, therefore, gas flows are typically faster than liquid flows. On the other hand, the speed of a sonic signal as it travels through a gas is slower than when it travels through a liquid. Because the speed of a sonic signal through a liquid is so much greater than the flow rate of the liquid through a pipe, the physical effects of the flow stream in delaying the sonic signal do not prevent the meter from attaining the specified accuracy. In a gas, however, the speed of the sonic signal may be one or more orders of magnitude closer to the gas flow rate, and the physical effects of the gas flow in delaying the sonic signal will significantly affect the accuracy of the measurement.
A basic ultrasonic flow meter for liquids is shown and described in Lee, U.S. Pat. No. 3,935,735, issued Feb. 6, 1976, and assigned to the assignee of the present invention. This meter uses a pair of transducers mounted on opposite sides of a diametrical section of a pipe, with one of the transducers being positioned downstream from the other. This sets up a diagonal ultrasound path from one transducer to the other. Each transducer is both a transmitter and a receiver of an ultrasonic pulse train. In transmission, electrical signals are converted by the transducers to sound waves, while in reception, the transducers convert sound waves to electrical signals. Two pulse trains are transmitted at opposite ends of the ultrasound path and are received a short time later at their opposite destinations.
Each ultrasonic pulse train travels across the flow stream at approximately the speed of sound through the particular liquid medium. Depending upon the flow velocity of the medium in the longitudinal direction through the pipe, the travel time will be shortened slightly for travel in the downstream direction and travel time will be lengthened slightly for travel in the upstream direction. For pipes of small diameter, the total travel time for the ultrasonic wave is very short. The measurement of small changes in travel time of the ultrasonic wave is a basic technical problem in metering flow rate.
As explained in the Lee patent, a mathematical relationship has been developed in which the flow rate is expressed as a function of elapsed travel times for the two ultrasonic pulse trains, and further as a function of the difference between the travel times in the upstream and downstream direction, respectively. The flow rate (V') along the axis of a pipe is related to the flow rate (V) along an acoustic path L by the sine of an angle .theta., which is the angle of the diagonal acoustic path relative to the axis of the pipe. With .theta. as some preselected, known angle, the flow rate (V') in the axial direction can be expressed in terms of some constant (K), the difference between the two travel times (T.sub.21 -T.sub.12) and the product of the two travel times (T.sub.12 and T.sub.21) as follows: ##EQU1##
In a pipe with a diameter of one foot, and a medium in which the speed of the sonic wave is 5000 feet/second when the full-scale fluid flow is 2.5 feet/second, the difference between the two travel times is 0.2 microseconds (0.2.times.10.sup.-6 seconds). For an accuracy of 1% of full scale, a difference in travel times of 2 nanoseconds (2.times.10.sup.-9 seconds) must be detected.
The times of travel, T.sub.12 and T.sub.21 in equation (1), can be expressed in terms of the path of travel (L), the speed of sound in the gaseous medium (c) and the flow rate of the gas (V) along the path (L) as follows: ##EQU2##
In the Lee patent, an assumption was made that c&gt;&gt;V and V'. This meant that either T.sub.12 or T.sub.21 could be taken to be L/c and that either one of the two travel times, T.sub.12 or T.sub.21 could be squared to obtain the denominator of equation (1) above.
The same assumption cannot be made for measurement of gas flow. The magnitude of V is not negligible in comparison with the sonic velocity (c). Also, the flow of the gas generates strong components that cross the acoustic path. This causes the phenomenon of "long pathing" of the sonic signal as it travels across the gas flow, and also causes the generation of noise in the acoustic path.
In the long pathing condition, the sonic signal does not follow the path L, the shortest path between two transducers. Instead it deviates from the path L, due to the greater effect of the velocity of the flow stream. While it moves generally in the direction of the path L, it travels a greater distance, which might be conceived as an arcuate path between the two transducers.
Noise may be caused by local turbulent flows which cause a number of small deviations from the shortest path for L. This might be thought of as zig-zag path that crosses the path L numerous times. Again, the result is that the acoustic signal travels a longer distance than L.
Long pathing and noise each have the effect of extending travel times. In effect, an error would be present in the travel times T.sub.12 and T.sub.21 used in the calculation of equation (1) by presently available metering equipment, and this error has been an obstacle to applying ultrasonic flow meters to the high accuracy measurement of gas.
Any errors in T.sub.12 are usually also included in T.sub.21 so they are cancelled from the numerator of equation (1). In the denominator of equation (1) any errors are magnified by the multiplication.
The Lee patent further discloses that the difference in the two travel times (the numerator in equation (1) can be measured by detecting the difference in electrical phase (.PHI..sub.21 -.PHI..sub.12) of two relatively lower frequency signals that can be extracted from higher frequency ultrasonic signals. Thus, equation (1) above can be rewritten as follows, where K' is different constant than K in equation (1): ##EQU3##
The resolution of phase differences has recently been improved in a microcomputer-controlled flow meter disclosed in U.S. Pat. application Ser. No. 716,471, filed Mar. 27, 1985. However, a significant inaccuracy would still be encountered in attempting to measure the flow of gas, due to the enlargement of errors in the denominator for the reasons explained for equation (1).
A seemingly unrelated problem in measuring gas flows arises from the supercompressibility of gas at higher pressures. Boyle's law concerning ideal gases is expressed in the following well known equation of state: EQU PV=nRT (5)
where:
P=pressure PA1 V=volume PA1 n=number of moles (units of molecular weight) PA1 R=the universal gas constant PA1 T=temperature
In the physical world this equation is only a fair representation at moderate pressure and at temperatures near those at which gas condenses to a liquid. At the temperatures and pressures present in the typical gas transmission and distribution lines, equation (5) is replaced by the following equation defining a new factor Z, which is referred to as the compressibility factor: ##EQU4##
For an ideal gas, Z=1 and the deviation of Z from unity is a measure of the deviation of the actual relation from the ideal equation of state. More complicated equations of state have been developed to determine the compressibility factor Z based on pressure, volume or temperature readings and based on coefficients that account for the nonlinear behaviour of these variables in relation to one another. The coefficients for these equations are provided in reference tables, which can be used in conjunction with readings to calculate Z-factors. Z-factors have also been determined from graphs developed from empirical data for specific substances as a function of pressure, for example.
Now, a device referred to as a Z-meter has been developed to measure the compressibility of a gas. Until recently, gas meter readings were multiplied by Z-factors determined from the tables to estimate true readings. The introduction of the Z-meter has automated the determination of Z-factors.
The Z-meter uses a load cell which includes an enclosure of a known volume (V). Gas at operating temperature and pressure is diverted from a pipeline into the enclosure. A weighing device is attached to the enclosure to sense the weight W (mass x acceleration of gravity) of the known volume (V) of gas, and this permits a determination of the mass per volume, which is the volume density (p). Pressure and temperature sensors are also attached to the enclosure to sense the pressure and temperature of the sample of gas in the enclosure. The Z-meter also includes a device for sensing the molecular weight of one mole of the gas. Having sensed all these variables, the Z-meter can calculate the Z factor for the sample of gas in the load cell.